(Multi-stage walking route)
From her home H located at (−2km,1km), a student walks straight to her school S at (3km,1km) and then to a public library L at (3km,−4km).
(i) Write the position vectors rH, rS and rL in unit-vector notation.
(ii) Obtain the displacement vector for the journey from H to S.
(iii) Calculate the resultant displacement HL for the complete trip H → S → L. Hence find its magnitude and the angle it makes with the positive x-axis.
(iv) Find the total distance actually walked by the student along the two straight segments and compare it with the magnitude of the resultant displacement obtained in part (iii).